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### Unit 3: Lesson 9

Lesson 12: Solutions to linear equations

# Solutions to 2-variable equations

The solution of an equation with one variable is a number. How does the solution of a 2-variable equation look like? Well, it is an ordered pair. Learn more about it and how to test solutions to 2-variable equations.

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• serious question . Does anyone actually use this ? if so for what ? cus honestly i dont see the point
• Yahy,

Solving linear equations is a foundation step for solving systems of linear equations, which is a foundation step for linear programming (which, surprisingly, is not computer programming) or linear optimization.

Linear programming is a method for calculating an optimal result given a set of constraints. Linear programming is used in business all the time.

For example, if you owned a shop, you might want to know the best combination of items to stock in the limited capacity of the shop in order to maximize cash flow. Your most profitable item might not be the best selling or your space might only hold 10 of your most profitable item or 40 of a less profitable item. Linear programming helps you to determine whether to stock 5 of the most profitable item and 20 of the less profitable item or 4 of the most profitable and 30 of the less profitable to keep the cash flowing steadily.

If you don't own the shop, but you work there, you want your boss to be able to do linear programming so there is money for you to be paid.

If you are able to do the linear programming, you would be able to see whether the boss has the right idea and, perhaps, you could make a suggestion that will get you a raise.
• I need some examples of linear equations in 2 variables
• this video helps but I could use more help
• WHY is this so confusing? Sinks into Confusion
• Is there a way to solve for x and y to find the correct value of x and y? At , is the only way to solve these two variable equations with plugging in each answer khan academy gives us?
• Yes, you can directly find points that are solutions to an equation. This is just an intro video to show you how to recognize if a point is a solution or not. It is useful to understand this to check your work. The videos that follow this one will show you how to directly find points that are solutions to the linear equation.
(1 vote)
• How can I solve an equation with two variables? An equation like ' 2x + 4y =100 solve for y and x '
• Solving for a variable is also called isolating the variable, so you want to move everything away from it.
To isolate y, first subtract 2x from both sides (4y = -2x + 100), then divide by 4 (y = -1/2 x + 25). This is the more common usage because this is a linear function in slope intercept form - y in terms of x or y dependent on x.
To solve for x, subtract 4y from both sides (2x = - 4y + 100), then divide by 2 (x = - 2y + 50).
• Is there a way to find two variables without options given
eg:- 4y+5x=12 but without options given
• If the goal is to find x and y intersection, one question can't answer that. You must have at least 2 equations to solve the two variables, since you can't have an intersection point w one equation.

hope that helps !